Today we’re going explore Smith Chart basics, and then use that information to learn about
the RF performance of a paperclip. Would this make a good antenna, at what frequencies does
it resonate? A Smith chart makes this really easy to see.
Let’s start with the Smith Chart, or you could use a Mr. Smith chart.
Real quick - if EE topics are up your alley please consider subscribing to this channel,
we’ll do a giveaway when we hit 100k subscribers and we’re super close!
Smith Charts look scary at first, but they’re not once you know what’s going on. Let’s
start with a complex impedance, say .5 + j1.1. If you plot out this impedance on the complex
plane, our X-Axis is our real component, or resistance, and the Y-Axis is our imaginary
component, or inductance and capacitance. Inductors are positive, capacitors are negative.
And you can plot it! We see where our real component .5 and our imaginary component,
1.1, meet, and we plot it. Simple Algebra 1 stuff.
A smith chart is basically this graph, but you curl it in on itself into a circle.
This might seem weird, because all of these axis go to infinity. It would be hard to plot
infinity resistance on this, but with the Smith Chart we can. And, an open circuit is
infinite resistance, infinity is not some weird edge case for electronics – open circuits
are everywhere! So to plot the same .5 + j1.1 on the Smith
Chart, we do the same thing we did before, we find .5 on the real axis, and +1.1 on the
imaginary axis and draw a spot where they meet. It’s Algebra 1 but it’ll impress
and confuse all the business majors. We have an open circuit – infinite impedance
on the far right, and a short circuit or 0 impedance on the far left. And literally everything
in between. The Smith chart now gets more complicated
for two reasons. Reason number one is that all this is normalized information.
For example, RF folks like 50 ohm systems, so if we had an impedance of 75 + j40, we’d
end up with a normalized impedance of 1.5 + j.8 and we can plot it.
In an ideal world, our generator and load are impedance matched, so we end up with 1
+j0 right in the middle. We get the best transmission, the transmission coefficient is 1, the reflection
coefficient is 0, and our vswr is 1. The Smith Chart tells us that! We can also use this
information to design impedance matching networks to move a point from non-ideal to ideal. This
is easier with a combined smith chart that has both impedance and admittance, but we’re
not going there today. The second reason this gets complicated is
that impedance is dependent on frequency. And everything is a combination of resistance,
inductance, and capacitance. So, naturally, as our frequency changes so does our impedance.
So at one frequency we have one nice point, but in RF engineering we care about a range
of frequencies so we often end up with some sort of curve as our frequencies change. This
is really nice, though, because we get a picture of our system as frequencies change.
Instead of more theory, let’s look at what this paperclip looks like on the Smith Chart
using a VNA. What the VNA does is output a known frequency and power and sees what it
gets back. We’ll solder our paperclip to this SMA adapter,
hook it up, and see what happens